Determine how many solutions exist for the system of equations. ${-12x-2y = 12}$ ${2x+2y = 18}$
Convert both equations to slope-intercept form: ${-12x-2y = 12}$ $-12x{+12x} - 2y = 12{+12x}$ $-2y = 12+12x$ $y = -6-6x$ ${y = -6x-6}$ ${2x+2y = 18}$ $2x{-2x} + 2y = 18{-2x}$ $2y = 18-2x$ $y = 9-x$ ${y = -x+9}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = -6x-6}$ ${y = -x+9}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.